If the sum of an infinite GP , a , a r , a r 2 , a r 3 , … is 15 and the sum of the squares of its each term is 150 , then the sum of a r , 2 a r 4 , a r 6 , … is:

Step-by-step solution

Given: a + a r + a r 2 + a r 3 + . . . . . . ∞ = 15 ⇒ a 1 - r = 15         . . . . 1 And, a 2 + a 2 r 2 + a 2 r 4 + a 2 r 6 + . . . . . . ∞ = 150 ⇒ a 2 1 - r 2 = 150 ⇒ a 1 + r a 1 - r = 150 ⇒ a ( 1 + r ) = 10       . . . 2 Solving equation ( 1 ) and ( 2 ) , we get r = 1 5 ⇒ a = 12 Now, a r 2 + a r 4 + a r 6 . . . . . . ∞ = a r 2 1 - r 2 = 12 × 1 25 1 - 1 25 = 1 2